Question: Simplify the following expression and state the condition under which the simplification is valid: $a = \dfrac{k^2 - 7k}{k^2 - 9k + 14}$
Explanation: First factor the expressions in the numerator and denominator. $ \dfrac{k^2 - 7k}{k^2 - 9k + 14} = \dfrac{(k)(k - 7)}{(k - 2)(k - 7)} $ Notice that the term $(k - 7)$ appears in both the numerator and denominator. Dividing both the numerator and denominator by $(k - 7)$ gives: $a = \dfrac{k}{k - 2}$ Since we divided by $(k - 7)$, $k \neq 7$. $a = \dfrac{k}{k - 2}; \space k \neq 7$